Version v0.5.9 · 18 parameters · 36 open caveats · confidence 5.5/10
A Fokker–Planck equation with jump process. This describes how a probability distribution over civilization states evolves over time — with drift (predictable trends), diffusion (random fluctuations), and jumps (crises and collapses).
n
relative population (demographic pressure)
w
wage share of GDP (labor vs. capital distribution)
e
elite fraction (overproduction indicator)
d
debt-to-GDP ratio (fiscal fragility)
U
urbanization rate
π
political polarization index
T
institutional trust (0–1)
κ
network connectivity (information propagation)
Layer 1 — Micro-Foundation
Defines the 'particle parameters' Θ — probability distributions governing individual human choice. Loss aversion, temporal discounting, conformity pressure, authority deference, in-group favoritism. These parameters feed into the drift equations as behavioral constants.
Θ = {λ, β_td, γ_conf, α_auth, γ_status, ...}
Layer 2 — Meso-Structure
Defines how individual parameters aggregate into collective dynamics. Network topology G_t determines cascade thresholds and propagation speeds. The computational sociologist identifies the drift equations A_1, A_2, A_3 describing population, wage, and elite dynamics through the limit-cycle (Turchin secular cycle) framework.
G_t = (N_t, E_t, w_ij, c_ij, φ_i)
Layer 3 — Macro-Dynamics
Supplies the empirical backbone — historical patterns that the formula must reproduce, economic power laws (Pareto distributions, debt cycles), and the institutional vector I_t that modulates drift through regime type, veto players, and bureaucratic capacity.
I_t = (R_t, V_t, B_t, P_t, X_t)
Layer 4 — Formalization
Builds the mathematical backbone: the Fokker–Planck equation with jump process, the Ito-corrected PSI stress index, diffusion tensor, and the Bayesian confidence architecture that converts model outputs into honest probabilistic forecasts with calibrated intervals.
Ψ = MMP × EMP × SFD (Ito-corrected)
Cross-Cutting — Epistemology
Attacks every output for curve-fitting masquerading as theory. Enforces falsifiability requirements, detects circular validation, distinguishes causal from correlational claims, and approves or rejects every formula update. No version of CURRENT.md can be committed without philosopher approval.
Verdict ∈ {APPROVE, APPROVE_WITH_CAVEATS, REJECT}
Every parameter with its current estimate, confidence, and layer origin. Parameters marked with open disputes need further validation.
| Symbol | Name | Value | Layer | Confidence | Sources |
|---|---|---|---|---|---|
| λ | Loss aversion coefficient | LogNormal(0.55, 0.35) | micro | 72% | 8 |
| β_td | Temporal discount factor | Beta(6, 2) | micro | 68% | 6 |
| γ_conf | Conformity pressure | sigmoid(x; 0.3, 3.5) | micro | 65% | 5 |
| α_auth | Authority deference 1 open dispute(s) | 0.61 ± 0.12 (HYBRID floor+overlay) | micro | 55% | 7 |
| c_coop | Cooperation frequency invariant | 0.613 ± 0.089 | micro | 82% | 12 |
| γ_ig | In-group favoritism | 0.58 ± 0.15 | micro | 70% | 9 |
| α_pareto | Pareto wealth exponent 1 open dispute(s) | 1.5 ± 0.3 (fat tail) | macro | 75% | 14 |
| T_ineq | Inequality accumulation timescale 1 open dispute(s) | ~125 yr | macro | 52% | 6 |
| T_secular | Secular cycle period 1 open dispute(s) | [150, 265] yr (damped-spiral interpretation) | macro | 62% | 11 |
| E_threshold | Elite overproduction threshold | 0.015 (1.5% of population) | macro | 60% | 7 |
| λ_0 | Jump rate baseline 1 open dispute(s) | 0.015/yr | formalize | 40% | 8 |
| Ψ_threshold | PSI crisis threshold 1 open dispute(s) | 0.7 | formalize | 45% | 9 |
| k_jump | Jump rate exponential sensitivity 2 open dispute(s) | LogNormal(log(2.5), 0.4) | formalize | 38% | 5 |
| η_pareto | Tempered-Pareto diffusion coupling 2 open dispute(s) | LogNormal(log(0.5), 0.8) — PROVISIONAL | formalize | 25% | 3 |
| b_min | Subsistence wage regularization floor 1 open dispute(s) | 0.03 (revised from 0.05) | formalize | 50% | 4 |
| β_U | Urbanization convergence rate 1 open dispute(s) | 0.020/yr | macro | 40% | 5 |
| π_path | Institutional path dependence | 0.96 | macro | 65% | 8 |
| δ_prop | Propaganda effectiveness | Beta(2, 5) → mean 0.28 | macro | 55% | 6 |
OVERFITTING REGIME FORMALLY DIAGNOSED: p≈42 free parameters, n_eff≈6–14 independent observations. Practical R² ceiling ≈0.05–0.15 at 1yr horizon. PARAMETER FREEZE enacted (net-zero budget — nothing new without retiring existing). Prior catalog expanded 20→27. Circular audit expanded 4→7 parameters; all 4 fully circular params concentrated in the jump process J[P]. b_min revised 0.05→0.03; k_jump recalibrated 3.0→2.5 (preliminary non-Turchin MLE). 3-tier out-of-sample validation protocol (LOOCV / Blocked-CV / CPCV) designed. Epistemological confidence revised down 5.8→5.5/10. No new Polymarket predictions — internal moratorium until calibration improves.
C13-1 STRUCTURALLY RESOLVED: 6 independent non-Turchin cases (Mughal, Meiji, Iran, Weimar, Rwanda, Spain) — 6 PASS / 2 PARTIAL / 0 FAIL. β_U = 0.020/yr defined: 8/8 drift coefficients now have estimates. Zone-conditional PSI validity framework.
FIRST PHILOSOPHER LEAD SESSION. Falsifiability 6/10; overfitting risk MODERATE-HIGH. 5 formula changes: scope boundary, PSI causal note, circular flags, rho_DA/chi_horm to Theoretical Scaffolding, Venezuela reclassified.
C7-1 PSI ITO RESOLVED (12-session journey). Full dΨ SDE derived, sympy-verified. Novel w=0.5 sign-change prediction. CROSS-013 downgraded CRITICAL→HIGH. Period revised [150, 265]yr.
F_pol (A_6 polarization drift) APPROVED with surgical fixes. Limit-cycle period FORMALIZED [165, 327]yr envelops empirical [160, 335]yr.
Limit-cycle reframe APPROVED: Turchin phases are quadrants of ONE limit cycle (Hopf bifurcation). Period discrepancy mechanism identified (3 factors). FINAL BOOTSTRAP SESSION.
All Section A defined: α_pareto=1.5, α_tail=3.0, m_crash=0.33, T_debt 7yr/75yr, T_ineq~125yr. 5/6 drift coefficients specified. α_tail~3 validates FP+jump architecture.
CRIT-01 RESOLVED: 10D → 8D state vector (Ψ and φ now observables). CRIT-02 PARTIALLY RESOLVED: jump kernel formalized. γ_conf sigmoid form APPROVED.
9/13 Θ_fixed defined. HYBRID floor+overlay model for evolutionary constants. Cooperation invariance (Spadaro 2022: 70 societies) — STRONGEST finding.
Institutional vector I_t = (R_t, V_t, B_t, P_t, X_t) fully defined. Per-equation drift modulations A_1–A_8 with institutional constraints. π_path=0.96; δ_prop specified.
Bayesian Confidence Architecture defined (Section 6). Prior catalog: 12 informative + 8 placeholder. First prediction: NATO exit P=2.5% [0.5%, 8%] vs market 10%.
8 macro parameters defined: λ_0, Ψ_threshold, Ψ_critical, k_jump (jump process); T_secular (secular cycles); E_threshold (elite overproduction); F_fiscal; α_war. 5 Philosopher fixes applied.
14 micro-parameters defined. 4 critical parameters: λ (loss aversion), β_td (temporal discounting), γ_conf (conformity), α_auth (authority deference). 3 parameters flagged as replication failures.
Full FP+jump formalization. 10D state vector formalized. Three order parameters (PSI, phi, Gamma) defined. Turchin-PSI connection established.
Framework skeleton: Fokker-Planck + jump process architecture. 10D state vector proposed. PSI composite index architecture sketched.